Can the Potential Energy of an Electron in a Hydrogen Atom be Measured?

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SUMMARY

The potential energy of an electron in a hydrogen atom is defined as V = -e²/r, where e is the elementary charge and r is the distance from the nucleus. While direct measurement at a specific point is not feasible, experimental data from binding energy (BE) and electron-proton scattering provide validation for this potential energy formula. The discussion highlights the challenge of solving the Schrödinger equation when the potential energy is unknown, emphasizing the necessity of defining the Hamiltonian to determine eigenstates accurately.

PREREQUISITES
  • Quantum Mechanics fundamentals
  • Understanding of the Schrödinger equation
  • Knowledge of binding energy (BE) in atomic physics
  • Familiarity with electron-proton scattering experiments
NEXT STEPS
  • Research methods for measuring binding energy in hydrogen atoms
  • Study the implications of the Schrödinger equation in quantum mechanics
  • Explore electron-proton scattering techniques and their significance
  • Learn about Hamiltonians and their role in quantum systems
USEFUL FOR

Students and professionals in quantum mechanics, physicists studying atomic structures, and researchers interested in the measurement of atomic potential energies.

batsan
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It is known that the potential energy of electron in the hydrogen atom is completely definite quantity, for given point . How we can measure it?
 
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"How we can measure it?" You can't place an electron at point r to measure
-e^2/r, but there are other ways to measure that V=-e^2/r is correct.
It leads to the experimental BE and energy levels of hydrogen and to the correct experimental e-p scattering.
This can be considered a measurement that V= -e^2/r is correct.
 
Can you post me some links for this problem.
What is BE? May be Bose-Einstein?
How we can solve Schrödinger equation which have given wave function , but unknown pot. energy?
Thanks!
 
batsan said:
How we can solve Schrödinger equation which have given wave function , but unknown pot. energy?
Thanks!

I'm no expert on QM, but isn't the answer to this question simply, "you...can't!" I mean, if the Hamiltonian is not fully-defined, then you can't solve for its eigenstates.
 
Last edited:
Eigenstates are known. Unknown is only U(x).
 
batsan said:
What is BE?

I think Meir means "binding energy", that is, measurements of the ionization energies of hydrogen atoms.
 
Thanks!
Of course, it's "binding energy". I didn't guess right.
 

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